Theoretical evaluation of internal pressure in ternary and sub-binary liquid mixtures at various temperatures

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1 Available online at International Letters of Chemistry, Physics and Astronomy 4 (0) 8-95 ISSN Theoretical evaluation of internal pressure in ternary and sub-binary liquid mixtures at various temperatures J. Madhumitha, N. Santhi*, G. Alamelumangai, M. Emayavaramban Department of Chemistry, Government Arts College, C.Mutlur, Chidambaram 6080, India * address: nsaanthi@gmail.com ABSTRACT The Internal pressures of Ternary and their sub-binary liquid mixtures of benzene() + hexane() + sec-butyl alcohol(3) were calculated using density, velocity and molar refraction from the temperature range of 303.5K-38.5K. For the Binary liquid mixtures, the Experimental Internal pressure values were correlated through an equation proposed by Andiappan et.al. For the Ternary liquid mixture, the Experimental Internal pressure values were correlated through an equation proposed by us. The Experimental values and the Theoretical values are in close agreement with each other. Keywords: Ternary liquid mixtures, sub-binary liquid mixtures, benzene, hexane, sec-butyl alcohol. INTRODUCTION The Internal pressure is the cohesive force, which is a resultant of forces of attraction and forces of repulsion between molecules in a liquid, and considerable importance can be gained by simply observing and comparing internal pressure-volume curves for pure liquids.the term a/v in Vander waals equation being the measure of attractive force of the molecule is called the cohesive or internal pressure. The intermolecular forces give a liquid its cohesion and it creates a pressure of thousand to ten thousands atmospheres within a liquid. Cohesion creates a pressure within a liquid of between 0 3 to 0 4 atmospheres. The internal pressure thus depends markedly on the molar volume, and also on the external pressure. It should be emphasized that the internal pressure is also sensitive to the repulsive component in a liquid 3. Non-polar liquids have low internal pressures of the order of 000 to 3000 atm; polar liquids have somewhat larger values, hydrogen bonding still increasing the value, water having a value around twenty thousand atmospheres 3,4. The importance of internal

2 International Letters of Chemistry, Physics and Astronomy 4 (0) 8-95 pressure in understanding the properties of liquids and the full potential of internal pressure as a structural probe did become apparent with the Pioneering work of Hildebrand 5,6. In an excellent article Dack 7 reviewed the importance of solvent internal pressure and cohesion to solution phenomena. The internal pressure is a single factor which varies due to all type of solvent-solute, solute-solute and solvent-solvent interactions.the Various thermodynamic properties and molecular interactions involving self-associated alcohols and phenols helps in understanding the inter and intramolecular interactions. Stavely et al 8 compared the internal pressure of individual liquid components and predicted the interaction in liquid mixtures. Richards 9 pointed out the importance of internal pressure in understanding the physical properties of liquids and solids. An extensive list of values of internal pressure for liquids has been given by Allen et al 0.. MATERIALS AND METHODS The chemicals used in the present work are Analar grade and purified by the standard methods. The purity of samples are checked out by measuring their density, boiling point and refractive index ( Table.). Table. The Physical constants of pure liquids are given in the following table. Liquid Density(g/cm 3 ) Boiling point Refractive Index(n) K 98K ( C) 303.5K 308.5K Exp Lit Exp Lit Exp Lit n-hexane Benzene sec-butyl alcohol Ultrasonic velocities of pure liquids and liquid mixtures from the temperature range of 308K to 38K were measured using Ultrasonic Interferometer operating at 3 MHz. The density was determined at the experimental temperatures using 0 ml capacity specific gravity bottle immersed in a thermostatic bath (accuracy +0.0 C). The volume of the bottle at the experimental temperature, viz. 308K-38K was ascertained using doubly distilled water. 83

3 International Letters of Chemistry, Physics and Astronomy 4 (0) THEORY AND CALCULATION Srivastava and Berkowitz Equation equation was used to compute internal pressure from the measurement of ultrasonic velocity, density and refractive index. Srivastava and Berkowitz Equation is U D ' = K ( Rm) πi () Where: U = Ultrasonic velocity D = Density Rm = Molar refraction K' = distinctly structure dependent Constant π i = Internal pressure If the data for ultrasonic velocity, density, Molar refraction, internal pressure of pure liquids are known, the constant (K ) can be determined using equation (). Srivastava and Berkowitz Equation for the Binary Liquid Mixtures is ( π ) i = ( x K ' + U x K D ' ) ( Rm) () Where U =Ultrasonic velocity of the binary mixture D = Density of the binary mixture (Rm) = Molar refraction of the binary mixture x and x are Mole fractions of components () and () K ' and K ' are distinctly structure dependent constants (π i ) = Internal pressure of the binary mixture 84

4 International Letters of Chemistry, Physics and Astronomy 4 (0) 8-95 Evaluation of Rm: n xm + xm Rm = n + d (3) Where n = refractive index x and x are Mole fractions of components () and () m and m are Molecular weight of components () and () d = density The Andiappan et al 3 equation was used to calculate the theoretical internal pressure of binary liquid mixtures. Andiappan et al equation is logπ i x logπ x logπ βx = + (4) Where x and π are the mole fraction and internal pressure of the component and x and π are the mole fraction and internal pressure of the component. The equation (4) containing only one constant β, has been employed for correlating the experimental data. The experimentally determined internal pressure data for all the three binary systems have been correlated through equation (4) at temperatures 303.5K to 38.5K (Table 3). Constant β has been determined through a least square method at all the temperatures. Srivastava and Berkowitz equation for the Ternary liquid mixture is written as x ( π ) i 3 = ( x K ' + x U K 3 ' + x D 3 ' 3K3 ) ( Rm) 3 (5) Where U 3 =Ultrasonic velocity of the ternary mixture D 3 = Density of the ternary mixture (Rm) 3 = Molar refraction of the ternary mixture x, x and x 3 are Mole fractions of components (), () and (3) K ', K ' and K 3 are distinctly structure dependent constants (π i ) 3 = Internal pressure of the ternary mixture 85

5 International Letters of Chemistry, Physics and Astronomy 4 (0) 8-95 In the present work, the equation (4) for ternary system is modified as logπ = i x logπ + x x x ( β ( x logπ + x 3 3 x )) + x logπ + x x 3 3 x ( β ( x 3 3 ( β ( x x x )) Cx x x )) + 3 (6) Where β = binary interaction constant for, component β 3 = binary interaction constant for, 3 component β 3 =binary interaction constant for 3, component The constants β, β 3 and β 3 are determined from equation (4) using least square method. Constant C has been determined through a least square method at all the temperatures. 4. RESULTS AND DISCUSSION For the Ternary and sub-binary systems, the internal pressure values are evaluated from the temperature range of 303.5K to 38.5K. These values are correlated through equations (4) and (6) is shown in Tables ( & 3). Table. Experimental and Calculated Internal pressures(in atm) System benzene() + hexane() Mol Frac 303.5K 308.5K 33.5K 38.5K x EXP CAL EXP CAL EXP CAL EXP CAL

6 International Letters of Chemistry, Physics and Astronomy 4 (0) β = β = β = β = ABSD = 0.8% ABSD = 0.36% ABSD = 0.574% ABSD = 0.676% System sec-butyl alcohol() + hexane() Mol Frac 303.5K 308.5K 33.5K 38.5K x EXP CAL EXP CAL EXP CAL EXP CAL β = β = 0.08 β = β = ABSD = 0.949% ABSD = 0.884% ABSD = 0.773% ABSD = 0.895% System sec-butyl alcohol() + benzene() Mol Frac 303.5K 308.5K 33.5K 38.5K x EXP CAL EXP CAL EXP CAL EXP CAL

7 International Letters of Chemistry, Physics and Astronomy 4 (0) β = β = 0.08 β = β = ABSD = 0.949% ABSD = 0.884% ABSD = 0.773% ABSD = 0.895% Table 3. Experimental and Calculated Internal pressures(in atm) for the system benzene() + hexane() + sec-butyl alcohol(3) Experimental and Calculated Internal pressures(in atm) for the system benzene() + hexane() + sec-butyl alcohol(3) Mol Frac 303.5K 308.5K 33.5K 38.5K x x EXP CAL EXP CAL EXP CAL EXP CAL

8 International Letters of Chemistry, Physics and Astronomy 4 (0) C =.0370 C = C = C = ABSD = 0.986% ABSD =.0060% ABSD =.969% ABSD =.375% 89

9 International Letters of Chemistry, Physics and Astronomy 4 (0) 8-95 Both the Experimental and Theoretical Internal pressure values are represented in the tables ( & 3). It is known from the tables that both the experimental and the theoretical internal pressure values are more comparable with each other. By using least square method, the Interaction constants (β) and (C) are evaluated from the temperature range of 303.5K to 38.5K. The absolute average deviation between the experimental and correlated Internal Pressure values for all the binary systems varies from 0.7% to 0.38%. The Interaction constant (β) evaluated for all the binary systems varies from 0.0 to It is known from the tables () & (3) that the increase in internal pressure values with increase of alcohol concentration is probably due to Hydrogen bonding. Since alcohols are strongly self-associated liquid having a three dimensional network of Hydrogen bond 4. So it is apparent that when two interacting molecules are having some sort of attractive forces like that of hydrogen bonding should result in increase of internal pressure 5. The hydrogen bonding arises from short range interaction augmented by the fact that Hydrogen bond distance (A-H--B) is greater than Vander Waals radii. The short range forces arise when the molecules come close enough together causing a significant overlap of electron clouds and are often highly directional 6. The non-linear relationship is more obvious for sec-butyl alcohol and benzene. This may be due to the interaction of the delocalized π-bond electron cloud with the sec-butyl alcohol. Benzene is a non-polar and an inert aromatic solvent. The dissociation effect of benzene molecule prevents self-association in associated alcohol molecules. The π-electron cloud of benzene is responsible for the dissociation effect. The Internal pressure varies with respect to the concentration and Temperature. This is shown in graph. Figures -3 shows a linear variation of internal pressure with the concentration for binary liquid mixtures from the temperature range of 303.5K to 38.5K. Fig.. 90

10 International Letters of Chemistry, Physics and Astronomy 4 (0) 8-95 Fig.. Fig. 3. From the Tables & 3 it is known that the decrease in internal pressure values with increase of temperature is due to the decrease in cohesive forces. The reduction in internal pressure may be due to the loosening of cohesive forces leading to breaking the structure of the solute. 9

11 International Letters of Chemistry, Physics and Astronomy 4 (0) 8-95 When the temperature is increased, there is a tendency for the solute molecules to move away from each other, reducing the possibility for the interaction, which may further reduce the cohesive forces 7. Due to weakening of intermolecular forces of attraction the internal pressure should fall. This is an important observation which we have made and which is to be expected theoretically also as cohesive forces between molecules becoming less with increasing temperature 8. Figures (4-6) shows a linear variation of internal pressure with the reciprocal of temperature for binary liquid mixtures from the temperature range of 303.5K-33.5K. The absolute average deviation between the experimental and correlated values for the Ternary system varies from 0.98% to.37%. The evaluated Interaction constant (C) for the Ternary system varies from 0.89 to.03. Fig. 4. The average absolute deviation for the Ternary system is greater than that for the sub-binary system. This may be due to the Interaction between the three components. Among the three components, one of the component is self associated alcohol (sec-butyl alcohol). While the other two components (benzene and hexane) which are non-polar in nature. Hexane is a non-polar chain molecule; only Vander Waals type interactions are present in hexane, while alcohol molecule is polar and associate strongly through hydrogen bonding. The alcohol molecule associate in inert hexane medium and form clusters. An associated molecular cluster in a liquid may be called as a quasi-molecule or a pseudo molecule 9. While with benzene, π-bond interaction takes place with alcohol. Due to these strong interactions among the components in a ternary liquid mixture, the interaction constant values for the Ternary liquid mixture increases than that of the 9

12 International Letters of Chemistry, Physics and Astronomy 4 (0) 8-95 Binary liquid mixtures. This increase in Interaction constant values leads to increase in absolute average deviation for the Ternary system than that of the Binary system. Fig. 5. Fig

13 International Letters of Chemistry, Physics and Astronomy 4 (0) CONCLUSION It is evident from the present work, that The absolute average deviation between the experimental and correlated values for the Binary system and Ternary system varies from 0.7% to.37% indicating the applicability of equations (4) and (5). Internal pressure and their use in the study of molecular interactions. The character of association of alcohols makes the study of interactions particularly interest. The cohesive forces are of primary importance. REFERENCES [] Barton, A.F.M., J. Chem. Edu. 48(3), (97) 56 [] Vanderwaals, J.D., Essay on the continuity of the gaseous and liquid states London (873). [3] Suryanarayana C.V., J. Acoust. Soc. Ind. 7 (979) 3. [4] Suryanarayana C.V., J Acoust Soc India 5(4), (977) [5] Hildebrand J.H., Scott R.L., Solubility of Non-electrolytes, rd Edn., Reinhold, Publ.Corpn., New York, (950), P.. [6] Hildebrand J.H., Scott R.L., Regular Solutions, Prentice-Hall, Englewood cleffs, New Jersy, (96). [7] Dack M.R.J., Chem. Soc. Rev. 4(), (975) [8] Stavely L.A.K., Lupman W.J., Hart K.R., Faraday Trans. Soc. Diss., 5 (953) 30 [9] Richards T.W., Chem. Rev. (95) 35 [0] Allen G., Gee G., Wilson G.J., Polymer (960) 456 [] Weissberger A., Technique of organic chemistry Vol.7( nd edn), Interscience Newyork., (955). [] Srivastava S.C., Berkowitz N., Canadian Journal of Chemistry, 4 (963) [3] Amirthaganesan G., Govindasamy S., An Andiappan, Indian Journal of Chemistry Vol.5A (986) [4] Rowlison J.S., Liquid and Liquid mixtures, nd Edn.,Butter Worths, London, 59 (969). 94

14 International Letters of Chemistry, Physics and Astronomy 4 (0) 8-95 [5] Marimuthu S., Internal Pressure, Free Volume and Thermodynamic Studies of Molecular Interactions., M.Phil.Thesis, Department of Physics, Annamalai University (987). [6] Rajendran V., Ultrasonic studies on some Ternary systems and Rock Specimens, Ph.D Thesis, Annamalai University (99). [7] Kannappan A.N., Palani R., Ind. J. Pure Appl. Phys., 45 (7), (007) [8] Pugalendi K.V., A study of internal pressure of Binary liquid Mixtures from Ultrasonic Measurements, M.Phil Thesis, Annamalai University (983). [9] Vasantharani P., Muthu Shailaja S., Kannappan A.N., Ezhil Pavai R., Journal of Applied Sciences, Vol.8, Issue:, (008)